I used to work for a company that manufauctured weatherstrips for Ford, including this type. There is a roll-formed steel carrier inside, that the rubber is co-extruded over. This steel begins as an electrocoated band before it is roll-formed and rubber coated. Over time, the coating can break down, especially near the ends where it is die-cut in manufacturing, and water can eventually permeate. Looks like your belt line moulding has rust on the steel carrier. Just replace it with a good one; they're fairly easy to find in the salvage yards for a nominal charge.
There is one screw on the rearmost end of the strip, accessible from the door jamb. After the screw is removed, just gently pry up on the strip starting from the rear; it is retained the rest of the way with spring clilps. Be careful removing the screw; these are often rusted and stuck. If you strip the head out, you'll need to carefully take a Dremel tool, and grind off the head before you can remove the strip. When you buy a replacement, try to find one that isn't rusted badly in the screw hole.
Good Luck,
JD
